algebraic expressions

ratio of x cubed and the sum of y and 5 x cubed means we raise x to the power of 3: x^3 The sum of y and 5: y + 5 ratio of x cubed and the sum of y and 5 x^3/(y + 5)

Aliyah had $24 to spend on seven pencils. After buying them she had $10. How much did each pencil cost? Let p be the number of pencils. We're given the following equation: 7p + 10 = 24 To solve this equation for p, we type it in our math engine and we get: p = 2

4 multiplied by the cube of p is reduced by 5 The cube of p means we raise p to the 3rd power: p^3 4 multiplied by the cube of p 4p^3 reduced by 5: 4p^3 - 5

5 times quantity n minus 3 quantity n minus 3 (n - 3) 5 times quantity n minus 3 5(n - 3)

the sum of w and v divided by their difference the sum of w and v: w + v their difference: w - v the sum of w and v divided by their difference (w + v)/(w - v)

twice the sum of a and b is thrice c The sum of a and b: a + b twice the sum of a and b means we multiply the sum of a and b by 2: 2(a + b) Thrice c means we multiply c by 3: 3c The word is means equal to, so we set 2(a + b) equal to 3c: 2(a + b) = 3c

1/3c increased by the square root of d square root of d: sqrt(d) 1/3c increased by the square root of d 1/3c + sqrt(d)

twice a number subtracted from the square root of the same number The phrase a number means an arbitrary variable, let's call it x: x Twice a number means we multiply x by 2: 2x Square root of the same number: sqrt(x) twice a number subtracted from the square root of the same number sqrt(x) - 2x

the sum of 2 times x and 3 times y diminished by 12 2 times x: 2x 3 times y: 3y the sum of 2 times x and 3 times y 2x + 3y the sum of 2 times x and 3 times y diminished by 12 2x + 3y - 12

200 feet shorter than the height of a light house Let the height of a light house be h: h 200 fee shorter mean we subtract 200 from h: h - 200

3 is subtracted from square of a number The phrase a number means an arbitrary variable, let's call it x: x Square of a number means we raise x to the 2nd power: x^2 3 is subtracted from square of a number x^2 - 3

5 times a number is 4 more than twice a number The phrase a number means an arbitrary variable, let's call it x. x 5 times a number: 5x Twice a number means we multiply x by 2: 2x 4 more than twice a number 2x + 4 The word is means equal to, so we set 5x equal to 2x + 4 5x = 2x + 4

9x is subtracted from the sum of 3y and 4 The sum of 3y and 4 3y + 4 9x is subtracted from the sum of 3y and 4 3y + 4 - 9x

Write the sentence as an equation. 19 is equal to c less than 321 c less than 321: 321 - c The phrase is equal to means an equation, so we set 321 - c equal to 19: 321 - c = 19

thrice y plus x minus 2z Thrice y means we multiply y by 3: 3y plus x 3y + x minus 2z 3y + x - 2z

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions that accurately represent this scenario. We set up a proportion of inches to centimeters where i is the number of inches in 25 centimeters: 2/5 = i/25 To solve this proportion for i, we type it in...

decrease a number by 7 and multiply by 6. The phrase a number means an arbitrary variable, let's call it x: x Decrease a number by 7: x - 7 Multiply by 6 6(x - 7)

Add u and w, triple the result, then add what you have to v Add u and w u + w Triple the result means multiply the sum of u and w by 3: 3(u + w) Then add what you have to v: v + 3(u + w)

a taken away from 4b 4b - a

72 pounds and increases by 3.9 pounds per month Let m be the number of months. We write the algebraic expression below: 3.9m + 72